Fitxers

934690.pdf (425.86 KB)

Tipus de document

Article

Versió

Versió publicada

Data de publicació

2025-04-01

Llicència de publicació

cc by (c) Přenosil, Adam, 2024
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/228954

Pointed Lattice Subreducts of Varieties of Residuated Lattices

Títol de la revista

Autors

Director/Tutor

ISSN de la revista

Títol del volum

Recurs relacionat

https://doi.org/10.1007/s11083-024-09671-z

Resum

We study the pointed lattice subreducts of varieties of residuated lattices (RLs) and commutative residuated lattices (CRLs), i.e. lattice subreducts expanded by the constant denoting the multiplicative unit. Given any positive universal class of pointed lattices K satisfying a certain equation, we describe the pointed lattice subreducts of semi-K and of pre-K RLs and CRLs. The quasivariety of semi-prime-pointed lattices generated by pointed lattices with a join prime constant plays an important role here. In particular, the pointed lattice reducts of integral (semiconic) RLs and CRLs are precisely the integral (semiconic) semi-prime-pointed lattices. We also describe the pointed lattice subreducts of integral cancellative CRLs, proving in particular that every lattice is a subreduct of some integral cancellative CRL. This resolves an open problem about cancellative CRLs.

Matèries

Semàntica (Filosofia), Varietats (Matemàtica), Teoria dels reticles

Matèries (anglès)

Semantics (Philosophy), Manifolds (Mathematics), Lattice theory

Citació

Col·leccions

Articles publicats en revistes (Filosofia)

Citació

PŘENOSIL, Adam. Pointed Lattice Subreducts of Varieties of Residuated Lattices. Order. 2025. Vol. 42, núm. 1, pàgs. 87-114. ISSN 0167-8094. [consulta: 11 de maig de 2026]. Disponible a: https://hdl.handle.net/2445/228954

Exportar metadades

JSON - METS

Compartir registre